These days, everyone wants to be more confident. A few of the world’s most successful leaders are marked exceptions.

Ray Dalio is the founder of Bridgewater, the largest hedge fund in the world. His predictions about the markets come true so often, like his 2007 warnings of an imminent economic crisis, that he is sometimes referred to as the DaVinci of investing.

While Wall Street types are often notoriously cocksure, Dalio, on the other hand, is "always fearing being wrong." Bridgewater meetings frequently begin with experts second-guessing his decisions and end with Dalio changing his mind.

Admiral William McRaven successfully led the Seal Tim Six raid to get Osama Bin Laden. At the meeting where he first presented his plan, McRaven hedged, “Mr. President, we haven’t thoroughly tested this out yet, and we don’t know if we can do it, but when we do … I’ll tell you straight up.” The administration was surprised to learn that, unlike most military brass, McRaven was humble and unusually open to suggestion.

CEO of Amazon, Jeff Bezos, is exceptionally skeptical of his own projects. While many entrepreneurs are stubborn optimists, Bezos stands ready to quit at all times. In the case of Amazon Auctions, a category intended to compete with eBay, he quickly abandoned the idea after the data suggested potential failure. Bezos treats his views as temporary and encourages others to do the same by having ideas tomorrow that contradict their ideas today.

These examples might be surprising to hear. Great leaders, we’ve been taught, are supposed to have conviction in their beliefs. In fact, we often see a lack of confidence and a willingness to change our minds as a sign of weakness.

These leaders don’t care. As I reveal in my book,Persuadable: How Great Leaders Change Their Minds to Change the World, they know something that many others don't. An openness to being persuaded might not make you look like a great leader, but in a complex world that requires accurate decision-making, it's one of the most important qualities for being a great leader. The research backs them up.

In the most comprehensive study of its kind, Annenberg University Professor at the University of Pennsylvania Philip Tetlock meticulously tracked over 82,000 predictions of 284 experts for two decades in order to find out what makes some more accurate forecasters than others. Surprisingly, high performance had less to do with what the experts knew and more with how they thought.

He classified the experts into two different kinds of thinkers: hedgehogs and foxes. Hedgehogs "knew one big thing." They made forecasts based on grand theories about the world that they held with great confidence. When information contradicted their theory, rather than throwing out the theory, they threw out the information.

Foxes, on the other hand, "knew many little things". They were much less confident in their understanding of the world and were more willing to change their minds based on actual events -- even if it meant constantly contradicting themselves.

Foxes proved substantially more accurate than hedgehogs.

It's easy to see why, despite how it makes them look, Dalio, McRaven and Bezos are paranoid about keeping their confidence in check. They want to avoid being hedgehogs. This obsession gives them a competitive edge over their peers.

To foxes like them, confidence is neither good nor bad. Confidence is simply an expression of certainty in a particular belief.

When the leaders have more reason to believe that one of their opinions is right, for example when their idea survives a robust debate with their team, they allow themselves to have higher confidence. When their team provides them with solid reasons why their opinion is wrong, they lower their confidence. This foxy process of continually trying to match confidence level with the probability that an event will actually occur is called calibration.

Unlike everyone else, these leaders don't care about being more confident. What they desperately want to be is better calibrated. And it's this pursuit that has helped to make some of the most successful leaders in the world.

The stories of Dalio, McRaven and Bezos should be a lesson for any leader who wants to make more accurate decisions. Forget about the myth that leaders should be confident. Instead, focus on being calibrated.

If we look at the practices of these three men, we’ll see that one of the best ways to start is to argue with smart people. But don't argue to win -- argue to improve the accuracy of your beliefs. As Dalio says, "when two people disagree, logic demands one of them must be wrong. Why wouldn't you want to make sure that person isn't you?"